The jobs seems so similar, just on a smaller scale. So yeah. But ... like Pete Carroll said in hiring a coach, he'd rather have talent and enthusiasm than experience. You want a mediocre applicant who's been in the job, or a great one who has a learning curve? ... and President Obama seems to have required almost no learning curve. Maybe the POTUS job just comes with that many resources.
"Too strong a person" ... doubt I'd worry DaddyO. A CEO has been VP for most of her life, carrying out marching orders as directed. And as CEO she still has to accommodate the board, the stockholders, etc.
But yeah. Carly Fiorina is one of the most strong-willed (reasonable) power brokers I've seen in my life. In most aspects that's a big plus. Russell Wilson is an example. Folks like that push through obstacles that would stop me.